Flux observer-based control strategy for an induction motor

ABSTRACT

A method for regulating operation of an induction motor having a rotor includes calculating a rotor flux angle error value, via a flux observer of a controller, using estimated d-axis and q-axis flux values of the rotor, estimating rotor position using a position observer of the controller, and calculating slip position of the rotor using d-axis and q-axis stator currents. The method also includes estimating a rotor flux angle as a function of slip position and estimated rotor position, calculating a corrected rotor flux angle by selectively adding the rotor flux angle error value to the estimated rotor flux angle, and controlling output torque of the motor using the corrected rotor flux angle. A logic switch may be used to selectively add the rotor flux angle.

INTRODUCTION

An induction motor includes a stator and a bearing-mounted rotor thatare separated from each other by a small air gap. The non-linear natureof an induction motor's torque response can sometimes lead to increasedtorque error at higher speeds, with the term “torque error” describingthe difference between commanded and actual torque levels. The presentapproach is intended to address this potential control problem andthereby improve induction motor torque performance.

Generation and real-time control of a rotating magnetic field (RMF) isrequired for proper operation of an induction motor. The RMF cuts acrossconductive windings of the rotor to induce a periodic voltage in therotor's phase windings. Resultant currents in the phase windingsinteract with the RMF within the small stator-rotor air gaps to producetorque in the rotational direction of the RMF. Because torque generationoccurs when the rotor rotates at less than the RMF's speed, i.e., itssynchronous speed, induction motors are commonly referred to in the artas “asynchronous motors”.

Slip of a rotor in an induction motor is defined as the differencebetween the synchronous speed (ns) and the rotor speed (m), with slip(s) usually expressed as a percentage, i.e.:

$s = {\frac{n_{s} - n_{r}}{n_{s}} \times 100.}$

The synchronous speed may be expressed as:

$n_{s} = \frac{120f}{P}$

with P representing the number of poles of the induction motor and fbeing the frequency of the motor's polyphase supply voltage. Slip in aninduction motor may be difficult to accurately calculate under certainoperating conditions, which in turn may lead to the above-noted torqueaccuracy problem and other performance issues.

SUMMARY

A control strategy is disclosed herein for regulating operation of aninduction motor. The torque response of an induction motor may degradewith temperature, as well as with saturation or variation in motorcontrol parameters. For these and other reasons, the torque response ofan induction motor tends to be non-linear, with higher torque errorpossibly resulting at high motor speeds or under other conditions. Thepresent control strategy is intended to improve upon the current stateof the art of induction motor control by increasing torque linearity andaccuracy, as well as by providing other performance advantages asdescribed in detail below.

In particular, the disclosed methodology uses a flux observer in thesynchronous reference frame of the motor to estimate a rotor flux angleerror level for the induction motor, with the term “rotor flux angle”referring to the angle at which magnetic field lines intersect across-sectional area of the rotor's conductors. Flux angle error, whichis determined by a controller using estimated direct-axis (d-axis) andquadrature-axis (q-axis) rotor flux values, is then added to acalculated rotor flux angle to derive a corrected flux angle value. Thecorrected flux angle value is thereafter used in ongoing torque controloperations of the induction motor.

D-q axis transformation is a mathematical transformation technique thatis commonly used to simplify the analysis of polyphase electricalcircuits, e.g., three-phase alternating current (AC) circuits such asthose considered by the present disclosure. As will be appreciated bythose of ordinary skill in the art of motor controls, the d-axis is themotor axis on which magnetic flux is generated, while the q-axis is theaxis on which torque is ultimately generated. By convention, the q-axisleads the d-axis by 90°. Thus, d-axis and q-axis current commands issuedby the controller to the stator, and resultant d-axis and q-axiscurrents formed in the rotor, are regulated to produce a desired effecton the motor's torque operation.

Additionally, a dynamical model of a motor typically includes threereference frames: a stationary reference frame in which the d-axis andq-axis do not rotate, a rotor reference frame in which the d-axis andq-axis rotate at rotor speed, and a synchronous reference frame in whichthe d-axis and q-axis rotate at the synchronous speed of the inductionmotor. The above-noted flux observer, by operating in the synchronousreference frame, is thus rendered sufficiently robust to ongoing changesin rotor speed.

Control of the induction motor also requires accurate real-timecalculation of the rotor flux angle, with the flux observer of thepresent disclosure also helping to improve the accuracy of suchcalculations. That is, the flux observer estimates the d-axis and q-axisrotor flux and thereafter uses the estimated flux values to calculate arotor flux angle error value, e.g., as the arctangent of the d-axis andq-axis flux. Meanwhile, a rotor position observer operating in thestationary reference frame of the motor may be used to estimate rotorposition, i.e., the angular position of the rotor, using inputs from arotary position sensor. A corrected rotor flux angle is determined byapplying the rotor flux angle error to the estimated rotor flux angle.The corrected rotor flux angle is thereafter used to control operationof the induction motor.

In an example embodiment, a method for regulating operation of theinduction motor includes calculating a rotor flux angle error value, viathe flux observer of the above-noted controller, using estimated rotord-axis and q-axis flux values. The method also includes estimatingangular position of the rotor using a position observer of thecontroller, i.e., a state observer working in the motor's stationaryreference frame. The method further includes calculating the rotor'sslip position via the position observer using d-axis and q-axis statorcurrent commands from the controller.

As part of the example method, the controller estimates the rotor fluxangle of the rotor as a function of slip position and estimated rotorposition to generate an estimated rotor flux angle, and also calculatesthe corrected rotor flux angle by adding the rotor flux angle errorvalue to the estimated rotor flux angle. The controller then controlsoutput torque of the induction motor using the corrected rotor fluxangle.

The flux observer may calculate the rotor flux angle value as thearctangent of the d-axis and q-axis flux values.

Calculating the rotor flux angle error value may be performed by thecontroller as a function of the d-axis and q-axis currents and voltagesof the stator.

Optionally, a logic switch may be used having an ON state when amagnitude of the estimated d-axis flux value or the estimated q-axisflux value exceeds a calibrated threshold. The rotor flux angle errorvalue may be added to the estimated rotor flux angle when the logicswitch is in the ON state. Alternatively, the controller may beconfigured to apply a variable gain value at a magnitude of between 0and 1 to the rotor flux angle error value, with the magnitude of thegain value corresponding to a magnitude of the estimated d-axis orq-axis flux value.

Calculating a slip position of the rotor may include calculating therotor's slip frequency as a function of a predetermined electricalresistance and a predetermined inductance of the rotor, and apredetermined mutual inductance of the rotor and stator.

Controlling the output torque of the induction motor may includegenerating and delivering torque from the induction motor to a coupledload via the rotor. In some embodiments, the coupled load may be one ormore drive wheels of a motor vehicle.

An electrical system is also disclosed herein having the inductionmotor, a rotary position sensor, and a controller configured to executethe method noted above.

The above features and advantages and other features and advantages ofthe present disclosure are readily apparent from the following detaileddescription of the best modes for carrying out the disclosure when takenin connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic illustration of an example electrical systemhaving a polyphase induction machine coupled to a load and controlledvia a controller using a flux observer as set forth herein.

FIG. 2 is a schematic logic flow diagram of the controller shown in FIG.1.

FIG. 3 is a schematic logic flow diagram of a flux observer in thesynchronous time frame that is usable as part of the controller of FIG.2.

FIG. 4 is a flow chart describing an example method for implementing acontrol strategy using the flux observer shown in FIG. 3.

The present disclosure is amenable to various modifications andalternative forms, and some representative embodiments are shown by wayof example in the drawings and will be described in detail herein. Novelaspects of this disclosure are not limited to the particular formsillustrated in the above-enumerated drawings. Rather, the disclosure isto cover modifications, equivalents, and combinations falling within thescope of the disclosure as encompassed by the appended claims.

DETAILED DESCRIPTION

This disclosure is susceptible of embodiment in many different forms.Representative embodiments of the disclosure are shown in the drawingsand will herein be described in detail with the understanding that theseexamples are provided as a representation of the disclosed principles,not limitations of the broad aspects of the disclosure. To that extent,elements and limitations that are described, for example, in theAbstract, Introduction, Summary, and Detailed Description sections, butnot explicitly set forth in the claims, should not be incorporated intothe claims, singly or collectively, by implication, inference orotherwise.

For purposes of the present detailed description, unless specificallydisclaimed: the singular includes the plural and vice versa; the words“and” and “or” shall be both conjunctive and disjunctive; the words“any” and “all” shall both mean “any and all”; and the words“including,” “containing,” “comprising,” “having,” and the like, shalleach mean “including without limitation.” Moreover, words ofapproximation, such as “about,” “almost,” “substantially,”“approximately,” and the like, may be used herein in the sense of “at,near, or nearly at,” or “within 0-5% of,” or “within acceptablemanufacturing tolerances,” or any logical combination thereof, forexample.

Referring to the drawings, wherein like reference numbers correspond tolike or similar components throughout the several figures, an examplevehicle 10 is shown in FIG. 1. The vehicle 10 include an electricalsystem 12 having an electric machine in the form of an induction motor(M_(E)) 14, the operation of which is automatically regulated inreal-time by an electronic controller (C) 50. As described below withparticular reference to FIGS. 2-4, the controller 50 receives a set ofinput signals (arrow CC_(I)) and, responsive to the input signals (arrowCC_(I)), generates a set of output control signals (arrow CC_(O)),including a corrected rotor flux angle as detailed below with referenceto FIGS. 2-4. The control signals (arrow CC_(O)) ultimately increase,decrease, or maintain a level of motor torque (arrow T_(M)) produced bythe induction motor 14.

To perform its overall control efforts, the controller 50 is programmedwith a flux observer 55, i.e., a state observer of magnetic flux thatoperates in the synchronous frame of reference of the induction motor14. The controller 50 additionally includes a position observer 56,i.e., a state observer of angular position of a rotor (R) 16 of theinduction machine 14 that operates in the stationary frame of referenceof the induction motor 14. The flux observer 55 and the positionobserver 56 may be embodied as programmed control logic of thecontroller 50, for instance as depicted in FIGS. 2 and 3, with theexample control logic used in the execution of an example method 100 asset forth below with reference to FIG. 4.

The controller 50 of FIG. 1 may include one or more digital computerseach having a processor (P), e.g., a microprocessor or centralprocessing unit, as well as memory (M) in the form of read only memory,random access memory, electrically-programmable read only memory, etc.,a high-speed clock, analog-to-digital and digital-to-analog circuitry,input/output circuitry and devices, and appropriate signal conditioningand buffering circuitry. Although omitted for illustrative simplicity,the controller 50 may be electrically connected to a power supply withinthe electric system 12, such as an auxiliary battery (B_(AUX)) 36powered via a direct current (DC) auxiliary voltage bus 35.

The electric system 12 shown schematically in FIG. 1 is described hereinas being part of the vehicle 10 solely for the purpose of illustration,and thus without limiting the electric system 12 to vehicular use ingeneral or automotive applications in particular. Induction machinessuch as the induction motor 14 are widely used in differentmanufacturing environments, power plants, and in consumer products, aswell as in non-automotive applications such as rail vehicles, aircraft,and marine vessels, and therefore such applications may benefit fromextension of the present teachings.

The induction motor 14 may be embodied as a polyphase/AC inductionmachine having the rotor 16 and a stator (S) 19. The angular position ofthe rotor 16, and thus its rotational speed, may be measured at discretepoints using a rotary position sensor 17, with the position sensor 17outputting a measured position signal (arrow θ_(rm)) indicative of themeasured angular position of the rotor 16. The position signal (arrowθ_(rm)) may be communicated to the controller 50 over a low-voltagetransfer conductor or a wireless path.

In the illustrated vehicular application, the rotor 16 may beselectively coupled to an input member 18 of a transmission (T) 20 viaan input clutch 11, such as a friction clutch or a hydrodynamic torqueconverter. The transmission 20 may include one or more internal clutchesand gear sets (not shown) that ultimately transfer motor torque (T_(M))from the input member 18 to a transmission output member 22 to therebyproduce transmission output torque (T_(O)). Although not shown in FIG.1, the vehicle 10 may optionally include an internal combustion engineand/or additional electric machines which, depending on the operatingmode, may combine with the motor torque (T_(M)) to provide thetransmission output torque (T_(O)) at a desired level. The transmissionoutput torque (arrow T_(O)) is then transmitted to one or more driveaxles 24, which in turn are coupled to a load, in this instance a set ofdrive wheels 26.

As part of the electric system 12 depicted in FIG. 1, individual phasewindings of the induction machine 14 may be energized via a polyphasevoltage (VAC) that is present on an AC voltage bus 28. The polyphasevoltage (VAC) may be produced as part of a power inverter module (PIM)30 using internal semiconductor switching and signal filtering, e.g.,pulse width modulation, as will be appreciated by those of ordinaryskill in the art. DC supply voltage (VDC) to the PIM 30, also referredto as a DC link voltage, may be provided by a high-voltage battery pack(B_(HV)) 32 over a DC voltage bus 33, with the DC voltage bus 33possibly connected to a DC-DC voltage converter 34. The voltage outputof the DC-DC voltage converter 34 may be at the reduced/auxiliaryvoltage (V_(AUX)), e.g., 12-15V or another level suitable for storage inthe auxiliary battery (B_(AUX)) 36.

Referring to FIG. 2, control logic 40 is depicted schematically forimplementing the method 100 described herein, with an example embodimentof the method 100 shown in FIG. 4. The flux observer 55 includes a fluxcalculation block (“k”) 42, a flux magnitude calculation block (“MAG”)44, and a flux error calculation block (“{circumflex over (θ)}_(err)”)46 in the illustrated embodiment.

Outside of the flux observer 55, the position observer 56 includes arotor position estimation block (θ_(r)) 43, a slip calculation block(“ω_(SL)”) 45, and an integrator block

$\left( \frac{1}{s} \right)$

47. In a possible embodiment, the flux observer 55 is usedsituationally, such that operation of the flux observer 55 is triggeredusing an optional logic switch 59 having a logic state of 0/OFF or 1/ON,with the logic state being based on the output of the flux magnitudecalculation block 44. The logical switching operation is indicated bydouble-headed arrow SW. In an alternative embodiment, the flux observer55 may be used continuously, such that its output is weighted by avariable gain factor as explained below. The position observer 56 isactive regardless of the ON/OFF state of the optional logic switch 59.

Within the rotor position observer 56, control inputs to the slipcalculation block 45 include the commanded d-axis and q-axis currentsfor the stator 19 of the induction motor 14 shown in FIG. 1, with suchcurrents represented as arrows i_(d) and i_(q), respectively, and withthe d-axis and q-axis current values being in the synchronous referenceframe. Block 45 then calculates the slip frequency (ω_(SL)), forinstance as:

$\omega_{SL} = {{\frac{R_{r}}{L_{r}}\frac{L_{m}}{\lambda_{dr}^{e}}i_{qs}^{e}} \cong {\frac{R_{r}}{L_{r}}\frac{i_{qs}^{e}}{i_{ds}^{e}}}}$

where R_(r) is a predetermined electrical resistance of the rotor 16,L_(m) is a predetermined mutual inductance of the induction motor 14, Lris a predetermined inductance of the rotor 16, λ_(dr) ^(e) is the d-axisflux of rotor 16 in the synchronous reference frame (e), and i_(qs) ^(e)and i_(ds) ^(e) are the q-axis and d-axis currents (abbreviated as i_(q)and i_(d) in FIG. 2 for simplicity). Similarly, v_(qs) ^(e) and v_(ds)^(e) are the respective q-axis and d-axis voltages (abbreviated as V_(q)and V_(d) in FIG. 2 for simplicity) used as set forth below.

The integrator block 47 of FIG. 2 operates on the calculated slipfrequency (ω_(SL)) from block 45 to generate an angular slip position(θ_(SL)), which is then fed into a summation node 60. At summation node60, the slip position (θ_(SL)) is added to an estimated rotor position({circumflex over (θ)}_(r)), which is a value estimated by the rotorposition estimation block 43 using the measured rotor position (arrowθ_(rm)) as determined by the rotary position sensor 17 (also see FIG.1). The output of the summation node 60 is the estimated rotor fluxangle ({circumflex over (θ)}_(flx)), which is also referred to in theart as the indirect field-oriented control angle due to its use inindirect field-oriented control of the induction motor 14. The estimatedrotor flux angle ({circumflex over (θ)}_(flx)) is then fed into anothersummation node 61 and added to the output of the flux observer 55 tocalculate a corrected rotor flux angle (θ_(flx)) as a control output(see arrow CC_(O) of FIG. 1), which is thereafter used as the actualrotor flux angle in conducting torque control operations of theinduction motor 14.

With respect to the flux observer 55 of FIG. 2 and its constituent logicblocks 42, 44, and 46, the flux calculation block 42 is used tocalculate the d-axis and q-axis rotor flux values λ_(dr) ^(e) and λ_(qs)^(e) , abbreviated as λ_(d) and λ_(q) in FIG. 2 for simplicity, onceagain with the superscript “e” representing the synchronous referenceframe. The d-axis flux value may be determined in real-time by thecontroller 50 as follows:

$\lambda_{dr}^{e} = {\frac{\frac{L_{r}}{L_{m}}}{\left( \frac{R_{r}}{L_{r}} \right)^{2} + \omega_{r}^{2}}\left( {{\frac{R_{r}}{L_{r}}E_{d}} + {\omega_{r}E_{q}}} \right)}$

where E_(d) and E_(q) are the respective d-axis and q-axis components ofestimated back-EMF of the induction motor 14 individually defined as:

$E_{d} = {{R_{r}\frac{L_{m}}{L_{r}^{2}}\lambda_{dr}^{e}} + {\omega_{r}\frac{L_{m}}{L_{r}}\lambda_{qr}^{e}}}$$E_{q} = {{{- R_{r}}\frac{L_{m}}{L_{r}^{2}}\lambda_{qr}^{e}} + {\omega_{r}\frac{L_{m}}{L_{r}}\lambda_{dr}^{e}}}$

Similarly, the q-axis flux value may be determined as follows:

$\lambda_{qr}^{e} = {\frac{\frac{L_{r}}{L_{m}}}{\left( \frac{R_{r}}{L_{r}} \right)^{2} + \omega_{r}^{2}}\left( {{{- \frac{R_{r}}{L_{r}}}E_{q}} + {\omega_{r}E_{d}}} \right)}$

Also as part of the flux observer 55, the flux magnitude calculationblock 44 receives the d-axis and q-axis flux values from logic block 42and determines the respective magnitudes of each. At the same time, theflux error calculation block 46 uses the d-axis and q-axis flux valuesto calculate the rotor flux position error (θ_(err)), e.g.:

θ_(err) =a tan 2(λ_(dr) ^(e),λ_(qr) ^(e)).

The optional logic switch 59 shown in FIG. 2 may be configured to feedthe rotor flux position error (θ_(err)) forward to the summation node 61when the magnitude of the d-axis and q-axis rotor flux values (λ_(dr)^(e) or λ_(qr) ^(e)) exceeds a calibrated threshold. In this manner, theflux observer 55 may be implemented at specified torque operatingregions of the induction motor 14.

Alternatively, the rotor flux position error (θ_(err)) may becontinuously scaled by the controller 50 using a variable gain factorranging anywhere between and inclusive of 0 and 1, with such a gainfactor being indicative of or in proportion to the magnitude from block44. That is, the controller 50 may be configured to apply the variablegain value to the rotor flux position error (θ_(err)) at a magnitudecorresponding to a magnitude of the estimated d-axis flux value or theestimated q-axis flux value, e.g., the greater value thereof.

Referring briefly to FIG. 3, implementation of the flux observer 55 ofFIG. 2 is shown in further detail. Inputs may include a complex voltagevector (v_(dqs) ^(e)) and a complex current vector (i_(dqs) ^(e)),respectively depicted as (V_(dq)) and (I_(dq)) in FIG. 3 for simplicity,the latter of which is processed via a gain block 51, labeled Rs′ and again block 52 labeled σLs, i.e., the predetermined transient inductanceof the induction motor 14. The relevant variables are defined asfollows:

$v_{ds}^{e} = {{R_{s}^{\prime}i_{ds}^{e}} + {\sigma \; L_{s}\frac{{di}_{ds}^{e}}{dt}} - {\omega_{e}\sigma \; L_{s}i_{qs}^{e}} - {R_{r}\frac{L_{m}}{L_{r}^{2}}\lambda_{dr}^{e}} - {\omega_{r}\frac{L_{m}}{L_{r}}\lambda_{qr}^{e}}}$$v_{qs}^{e} = {{R_{s}^{\prime}i_{qs}^{e}} + {\sigma \; L_{s}\frac{{di}_{qs}^{e}}{dt}} + {\omega_{e}\sigma \; L_{s}i_{ds}^{e}} - {R_{r}\frac{L_{m}}{L_{r}^{2}}\lambda_{qr}^{e}} + {\omega_{r}\frac{L_{m}}{L_{r}}\lambda_{dr}^{e}}}$$R_{s}^{\prime} = {R_{s} + {R_{r}\frac{L_{m}^{2}}{L_{r}^{2}}}}$

The output of gain block 51 is subtracted at node 70 from the sum of thevoltage vector (v_(dqs) ^(e)) and the estimated back-EMF (E_(dq)) from acompensator block (“COMP”) 54, which is defined as E_(d)+jE_(q) incomplex vector form with the variable j being an imaginary term as willbe appreciated. Subtracted at node 70 is the output of a gain block 53(jω_(e)), with the variable ω_(e) being the stator frequency, and withthe gain block 53 applied to the output of an integrator block 37 asshown.

At node 71, the output of integrator block 37 is subtracted from theoutput of gain block 52, i.e., the product of the transient reluctance(σLs) and the complex current vector (i_(dqs) ^(e)), i.e., I_(dq). Theoutput of node 71 is fed into the compensator block 54 to calculate theestimated back-EMF (E_(dq)) noted above. The estimated back-EMF (E_(dq))is also fed into rotor flux calculator block 57 to determine the d-axisand q-axis rotor flux values (λ_(dr) ^(e) and λ_(qr) ^(e)) shown in FIG.2 (λ_(d) and λ_(q) in FIG. 3), and from there, to calculate the rotorflux position error (θ_(err)) via the rotor flux position errorcalculation block 46.

Referring to FIG. 4, the method 100 disclosed herein enables thecontroller 50 of FIG. 1 to regulate operation of the induction motor 14via targeted use of the flux observer 55 of FIGS. 2 and 3. An exemplaryembodiment of the method 100 commences with step S102.

At step S102, the controller 50 measures the angular position of therotor 16 from the rotary position sensor 17 and estimates, betweendiscrete measured positions, the rotor position ({circumflex over(θ)}_(r)). This occurs, once again, in the stationary frame of referenceof the induction motor 14. Step S102 may include processing the measuredrotor position (arrow θ_(rm)) of FIG. 1 from the rotary position sensor17 through the flux calculation logic block 43 of FIG. 2. The method 100then proceeds to step S104.

Step S104 includes calculating the slip frequency (ω_(SL)) via thecontroller 50, which is a calculation that may be performed according tothe equation provided above. The method 100 then proceeds to step S106.

At step S106, the controller 50 of FIG. 1 may compare the absolute valueof rotor speed from step S102 to a calibrated threshold, i.e., |{dotover (θ)}_(r)|≥CAL1. The method 100 proceeds to step S108 when thecalibrated threshold (CAL1) is exceeded, and to step S112 in thealternative when the calibrated threshold (CAL1) is not exceeded.

Step S108 includes running the flux observer 55 of FIGS. 2 and 3, and inparticular flux calculation block 45, to estimate the d-axis and q-axisflux values of the rotor 16, as abbreviated “λ CALC” in FIG. 4. Themethod 100 then proceeds to step S110.

At step S110, the controller 50 of FIG. 1 may compare the absolute valueof the flux values from step S110 to a calibrated threshold, e.g.,|λ|≥CAL2, with λ representing the values λ_(dr) ^(e) and λ_(qr) ^(e)(λ_(d) and λ_(q)) as noted above. In some embodiments, the individualmagnitudes may be compared to individual thresholds. Alternatively, thecontroller 50 may use the total flux magnitude in making the thresholdcomparison, e.g.:

|λ|=√{square root over (λ_(dr) ² +λe _(q) ^(r) r)}.

The method 100 proceeds to step S114 when the absolute value exceeds thethreshold, and to step S112 in the alternative.

Step S112 includes setting the rotor flux position error value to zero,i.e., θ_(err)=0. The method 100 then proceeds to step S116.

Step S114 includes calculating the rotor flux angle error (θ_(err)) viathe flux observer 55 as set forth above with reference to FIGS. 2 and 3,which as noted above is done using the estimated d-axis and q-axis fluxvalues. Calculation of the rotor flux angle error value may be performedby the controller 50 as a function of the d-axis and q-axis currents andvoltages of the stator 19 of FIG. 1. The method 100 then proceeds tostep S116.

At step S116, the corrected rotor flux angle (θ_(flx)) is calculated bythe controller 50 of FIG. 1, i.e., by selectively applying the rotorflux angle error value (θ_(err)) from step S114 to the estimated rotorflux angle ({circumflex over (θ)}_(flx)) output by node 60 of FIG. 2. Asnoted above, this may occur selectively using the logic switch 59 ofFIG. 2 or using a variable gain value indicative of the flux magnitudefrom block 44 of FIG. 2. The corrected rotor flux angle (θ_(flx)) isthen used in controlling the level of torque of the induction motor 14of FIG. 1.

That is, knowledge of the corrected rotor flux angle (θ_(flx)) enablesthe controller 50 to determine precisely when, and by how much, toincrease or reduce the d-axis and/i-axis currents, with weakening of thed-axis current serving to weaken the rotor flux. In turn, for aparticular DC link voltage, weakened flux enhances the ability toaccurately control the efficiency and power factor of the inductionmotor 14 as well as achieve a desired torque response. As such, themethod 100 and the associated controller 50 provide specificimprovements to computer-related technologies directed to real-timetorque control of the example induction motor 14 of FIG. 1.

Aspects of the present disclosure have been described in detail withreference to the illustrated embodiments. Those skilled in the art willrecognize, however, that modifications may be made without departingfrom the scope of the present disclosure. The present disclosure is notlimited to the precise construction and compositions disclosed herein.Thus, modifications apparent from the foregoing descriptions are withinthe scope of the disclosure as defined by the appended claims. Moreover,the present concepts expressly include combinations and sub-combinationsof the preceding elements and features.

1. A method for regulating operation of an induction motor having arotor and a stator, the method comprising: calculating a rotor fluxangle error value, via a flux observer of a controller, using anestimated d-axis flux value and an estimated q-axis flux value of therotor, wherein the flux observer operates in a synchronous frame ofreference of the induction motor; estimating an angular position of therotor, using a position observer of the controller, to thereby generatean estimated rotor position, wherein the position observer operates in astationary frame of reference of the induction motor; calculating a slipposition of the rotor, via the position observer, using a commandedd-axis current and a q-axis current of the stator; estimating a fluxangle of the rotor as a function of the slip position of the rotor andthe estimated rotor position to thereby generate an estimated rotor fluxangle; calculating a corrected rotor flux angle by selectively addingthe rotor flux angle error value to the estimated rotor flux angle; andcontrolling output torque of the induction motor via the controllerusing the corrected rotor flux angle.
 2. The method of claim 1, whereinthe flux observer is configured to calculate the rotor flux angle valueas an arctangent of the d-axis and q-axis flux values.
 3. The method ofclaim 1, wherein calculating a rotor flux angle error value is performedby the controller as a function of the d-axis and q-axis currents andd-axis and q-axis voltages of the stator.
 4. The method of claim 1,further comprising measuring the rotor position using a rotary positionsensor, wherein estimating the position of the rotor includes processinga measured rotor position from the rotary position sensor through a fluxcalculation logic block of the controller.
 5. The method of claim 1,further comprising a logic switch having an ON logic state when amagnitude of the estimated d-axis flux value or the estimated q-axisflux value exceeds a calibrated threshold, wherein the the rotor fluxangle error value is added to the estimated rotor flux angle when thelogic switch is in the ON logic state.
 6. The method of claim 1, whereinthe controller is configured to apply a gain value to the rotor fluxangle error value at a magnitude of between 0 and 1, and wherein themagnitude of the gain value corresponds or is in proportion to amagnitude of the estimated d-axis flux value or the estimated q-axisflux value.
 7. The method of claim 1, wherein calculating a slipposition of the rotor includes calculating a slip frequency of the rotoras a function of a predetermined electrical resistance of the rotor, apredetermined mutual inductance of the induction motor, and apredetermined inductance of the rotor.
 8. The method of claim 1, whereincontrolling the output torque of the induction motor includes generatingand delivering torque from the induction motor to a coupled load via therotor.
 9. The method of claim 1, wherein the coupled load is a set ofdrive wheels of a motor vehicle.
 10. An electrical system comprising: aninduction motor having a rotor and a stator; a rotary position sensorconfigured to output a position signal indicative of a measured angularposition of the rotor; and a controller programmed to regulate operationof the induction motor via execution of instructions, wherein executionof the instructions causes the controller to: calculate a rotor fluxangle error value, via a flux observer, using an estimated d-axis fluxvalue and an estimated q-axis flux value of the rotor, wherein the fluxobserver operates in a synchronous frame of reference of the inductionmotor; estimate a position of the rotor, using the position signal and aposition observer, to thereby generate an estimated rotor position,wherein the position observer operates in a stationary frame ofreference of the induction motor; calculate a slip position of therotor, via the position observer, using a d-axis current and a q-axiscurrent of the stator; estimate a flux angle of the rotor as a functionof the slip position and the estimated rotor position to therebygenerate an estimated rotor flux angle; calculate a corrected rotor fluxangle by selectively adding the rotor flux angle error value to theestimated rotor flux angle; and control output torque of the inductionmotor using the corrected rotor flux angle.
 11. The electrical system ofclaim 10, wherein the flux observer is configured to calculate the rotorflux angle value using an arctangent of the d-axis and q-axis fluxvalues.
 12. The electrical system of claim 10, wherein the controller isconfigured to calculate the rotor flux angle error value as a functionof the d-axis and q-axis currents and d-axis and q-axis voltages of thestator.
 13. The electrical system of claim 10, wherein the controller isconfigured to estimate the position of the rotor by processing ameasured rotor position from the rotary position sensor through a fluxcalculation logic block of the controller.
 14. The electrical system ofclaim 10, wherein the controller includes a logic switch having an onstate when a magnitude of the estimated d-axis flux value or theestimated q-axis flux value exceeds a calibrated threshold, wherein thecontroller is configured to add the rotor flux angle error value to theestimated rotor flux angle when the logic switch is in the on state. 15.The electrical system of claim 10, wherein the controller is configuredto apply a gain value at a magnitude of between 0 and 1 to the rotorflux angle error value, and wherein the magnitude of the gain valuecorresponds to a magnitude of the estimated d-axis flux value or theestimated q-axis flux value.
 16. The electrical system of claim 10,wherein the controller is configured to calculate the slip position bycalculating a slip frequency of the rotor as a function of apredetermined electrical resistance of the rotor, a predetermined mutualinductance of the induction motor, and a predetermined inductance of therotor, and then using the slip frequency to derive the slip position.17. The electrical system of claim 10, further comprising a load coupledto the rotor, wherein the controller is configured to generate anddeliver torque from the induction motor to the load via the rotor. 18.The electrical system of claim 17, wherein the electrical system is partof a motor vehicle, and wherein the coupled load is a set of drivewheels of the motor vehicle.